The veteran defensive tackle recently visited New England, and left town with a contract offer in hand, but ultimately decided that the Seattle Seahawks were a better fit for him. The interesting part of that equation, however, is that the Patriots actually made a stronger offer than Seattle, according to ESPN.

New England’s aggressive pursuit of Williams is interesting. The team has several defensive tackles, and if things work out, it could be one of the more crowded spots on the roster with Vince Wilfork, Tommy Kelly, Dominique Easley, Armond Armstead, Sealver Siliga, and Chris Jones competiting for roster spots and snaps.

However, Kelly (knee), Easley (knee), Armstead (unknown), and Wilfork (Achilles) are all fighting their way back from injuries. Wilfork took part in 11-on-11 drills last week in organized team activities, suggesting that he is on the right path.

If things do not work out, one of the deeper positions could become incredibly thin.

Williams, 33, spent his first 11 seasons with the Minnesota Vikings and finished last season with 29 tackles and 3.5 sacks. During a recent interview with Sirius XM, he detailed how the Patriots planned to use him.

"They had a lot of injuries and they have some veteran guys coming off of injuries that play tackle, and I would have a chance to compete for a position there,” Williams said. “Either way, we'd have a good rotation and have a chance to win some games."